Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C2×SD16 |
258 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^5,3^3|c^2=e,d^2=e,g^a=g^2,h^a=h^2,c^b=cd,d^b=de,f^b=f^2,h^b=h^2,d^c=de,g^f=gh43 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×((C3⋊D3)⋊C3)⋊C2, #13149961, #13149971, … |
| maximal normal subgroup of | SD16×((C3⋊D3)⋊C3)⋊C2, #13149961, #13149971, … |
| maximal quotient of | #13137899, #13137900, #13137914, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 1199);